Deciphering the Properties of Nanoconfined Aqueous Solutions by Vibrational Sum Frequency Generation Spectroscopy

When confined between walls at nanometer distances, water exhibits surprisingly different properties with reference to bare interfacial water. Based on computer simulations, we demonstrate how vibrational sum frequency generation (VSFG) spectroscopy can be used–even with very mild symmetry breaking–to discriminate multilayer water in wide slit pores from both bilayer and monolayer water confined within molecularly narrow pores. Applying the technique, the VSFG lineshapes of monolayer, bilayer, and multilayer water are found to differ in characteristic ways, which is explained by their distinct density stratifications giving rise to different H-bonding patterns in the respective solvation layers.


Simulation Details
Based on our earlier work on the dielectric properties of symmetrically confined water confined between two parallel graphene (GRA) sheets, 1 we designed for the present purpose asymmetric GRA-HBN slit pores by replacing one GRA wall by a hexagonal boron nitride (HBN) sheet. Compared to the previous study, we considerably increased the lateral extent of the slit pores to (x, y) = (34.7484, 34.3920)Å, now using 448 carbon atoms for the GRA sheets (instead of only 122) and, correspondingly, 224 boron plus 224 nitrogen atoms for the HBN walls. The fixed interlayer distance (d int ) between the GRA and HBN planes together with the number of water molecules (N Water ) has been determined as follows in order to generate a set of five representative confinement regimes from monolayer (XS: extra-small) to bilayer (S: small) to multilayer (M: medium, L: large, and XL: extra-large) water lamellae, see Table S1. These GRA-HBN slit pores compare closely in their interlayer distances and water density profiles to the corresponding set of symmetric GRA-GRA slit pores from Ref. 1, compare Table S1 in the present ESI and Fig. 1 in the present main text to Table S1 in the ESI and Fig. 3   To initiate the procedure leading to the final setups reported in Table S1, a supercell with (x, y) = (34.7484, 34.3920)Å and a z-dimension of 60Å has been setup where H 2 O molecules have been inserted one by one, starting from 40 up to 640 water molecules.
The "rigid piston" approach introduced in Ref. 1 (as explained in the ESI Section I.E therein) has been applied with an excess normal (perpendicular) pressure of 0.3 kbar (to establish the correct bulk water density, see ESI Section I.E.2) together with Nosé-Hoover thermostatting at 300 K (using a time constant of 0.04 ps) for 4 ns for each system setup.
Within these constant normal pressure simulations, the initially very large interlayer separation quickly decreases before it starts to fluctuate around a well-defined average value for the given fixed number of intercalated water molecules present within the respective slit pore. The corresponding final interlayer distances d int which are reported in Table S1 (and used in the subsequent "frozen piston" simulations 1 where the interlayer distances and thus the slit pore volume are kept constant by freezing all atoms in the perfectly coplanar GRA and HBN sheets in space as explained in the ESI Section I.E.4 therein) have been obtained by taking the average after excluding a 1 ns initial equilibration period for each rigid piston simulation. After fixing d int , each slit pore system is furthermore equilibrated in the canonical ensemble for another 2 ns. Each of these NVT simulation of the XS, S, · · · XL slit pore setups with the number of water molecules reported in Table S1 is then continued to generate a set of 20 initial condition by saving the trajectory every 80 ps. Subsequently, each of those is continued in the microcanonical ensemble for 500 ps, i.e. after switching off thermostatting, to generate 20 statistically independent NVE trajectories that allow us to rigorously compute time-correlation functions and thus proper VSFG spectra at 300 K (obtained as the average of all 20 independent spectra obtained from the NVE runs) as explained in the next sections.
Finally, in an effort to compare the VSFG response of the asymmetric GRA-HBN slit pores to the theoretically expected nil response of the symmetric GRA-GRA counterparts (which is nevertheless numerically nonvanishing due to finite sampling statistics leading to spectral noise), another 20 independent NVE trajectories have been generated for the symmetric GRA-GRA bilayer system S following the aforementioned protocol in order to compare one-to-one to the finite VSFG spectrum of the corresponding GRA-HBN bilayer pore.
For water, the SPC/E model 2 has been used whereas the force fields to describe the water/wall interactions for the HBN and GRA sheets are taken from previous work. 3,4 All S3 these force field simulations have been performed using the CP2k simulation package. 5,6

VSFG Calculations: Empirical Mapping Approach
We have used the well-established electronic structure/molecular dynamics (ES/MD)  In order to validate our ES/MD-based spectral calculations using the electric field mapping technique, we now compare the VSFG response from the bare HBN-water and GRA-water interface to that of the water-air interface in Fig. S1. The water-air surface has been generated here by removing the HBN and GRA sheets from the decoupled HBN-GRA system XXL and corresponding NVE trajectories have been produced with the water-air surface in substantial accord with earlier ab initio VSFG spectra obtained from AIMD simulations . 13 In particular, we refer to panel (a) of Fig. 1

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Furthermore, in an effort to analyze the origin of the zero VSFG signal for the symmetric GRA-GRA monolayer slit pore XS, we have dissected the spectral response in terms of "up", "down" and "parallel" orientations of the O-H chromophores following the same procedure as used in the decomposition underlying Fig. 3 in the main text (see its panel (a) for the definition of the three orientations) for the asymmetric GRA-HBN monolayer XS, which features a pronounced non-zero VSFG response. Unlike the asymmetric case, upand down-oriented O-H oscillators within the symmetric XS system produce numerically exactly the same VSFG signal but with opposite sign, which leads to the observed total cancellation that explains the overall zero response from that slit pore.

Quantifying Asymmetry in GRA-HBN Slit Pores
The extent of asymmetry of the water lamellae confined within the asymmetric GRA-HBN slit pore setups from XS to XL can be analyzed by comparing the water density along the surface normal with its mirror image. In case of the symmetric GRA-GRA reference slit pores depicted in the right panels of Fig. S4 for the XS to XL systems from top to bottom, we find perfectly symmetrically distributed density profiles with reference to the midpoint of two GRA sheets, thus providing an exact overlap with its mirror image (see the superimposed black and red solid lines) which also demonstrates that our sampling statistics is sufficient. In stark contrast, the minute difference in the interaction strength of water molecules with the HBN versus GRA sheets produces a slight asymmetry of the water density within the GRA-HBN slit pores as depicted in the left panels in Fig. S4. Therefore, even the very mild asymmetry in the water lamellae observed after replacing one GRA wall by HBN (compare the left to the corresponding right panels in that figure) is indeed able to produce finite VSFG responses as shown and discussed in the main text, which notably includes also the monolayer limit in the topmost panel where the asymmetry of the water density is barely visible. Moreover, this finding implies VSFG activity for a large variety of other asymmetric slit pore setups that offer stronger asymmetries due to more pronounced differences in their water-wall interactions and, thus, fruitful experimental prospects.

Interfacial and Intermediate Solvation Layers
Following the convention of our earlier work on symmetric GRA-GRA slit pores, 1 also in the context of the present asymmetric GRA-HBN systems water is found to be strongly stratified in terms of interfacial (IF) and intermediate (IM) layers depending on the width of the slit pores as depicted in Fig. 1

Decoupled HBN-Water and GRA-Water Surfaces
In order to calculate the VSFG reference spectra for bare HBN-water and GRA-water interfaces, we have generated a very large system in the slit pore geometry with twice the interlayer distance of the XL slit pore (namely d int = 39.32Å) as illustrated by Fig. S6(a).
It hosts N Water = 1400 water molecules and its interlayer distance is comparable to that of the XXL GRA-GRA slit pore from Ref. 1. The same protocol as described in Sec.
has been used to generate 35 statistically independent NVE trajectories that allow us to compute VSFG spectra.

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The separate VSFG spectral responses from the bare HBN and GRA interfaces with water can be calculated approximately by assuming a hypothetical dividing surface at at z = 0Å, i.e. equidistantly with respect to the HBN and GRA sheets. The two VSFG responses computed from the water molecules residing above (or below) that dividing surface, i.e. using those with positive (negative) z-values of their O positions, can be considered as the response from the bare HBN-water (or bare GRA-water) interface as reported in Fig. S6(b). Next, the corresponding difference VSFG spectra of such wall-water decoupled interfaces can be calculated by taking the difference of the spectral responses from the bare HBN-water and GRA-water surfaces which is depicted in Fig. S6(c). This difference spectrum serves as our intrinsic reference to probe the (de)coupling of the two interfaces within the XS to XL slit pore setups as detected with VSFG spectroscopy. Comparison with the total VSFG spectra of confined multilayer water as realized by slit pores XL and L down to M shows a negligible coupling of the interfacial water layers close to the HBN and GRA walls since these total spectra are all close to the reference. We conclude that no significant specific confinement effect is seen for these multilayer lamellae.
This is in stark contrast to the total VSFG spectra obtained from the XS and S systems (see Fig. 2(a) of the main text) which significantly deviate from the decoupled reference spectrum. Thus, the strong nanoconfinement effects on the structural dynamics and thus H-bonding of monolayer and bilayer water as a result of significant coupling effects between the HBN and GRA sheets in view of the molecularly small interlayer distances are clearly disclosed by VSFG spectroscopy and assigned as detailed in the main text.
Finally, if we take the difference between the difference VSFG signals from the two bare interfaces, GRA-water and HBN-water as already analyzed in the context of Fig. S6(c), and the VSFG signals from the confined water in asymmetric slit pores, we get double difference VSFG (ddVSFG) spectra which quantitatively disclose the characteristics of the confinement effect. As demonstrated by Fig. S7, the ddVSFG spectrum features S14 a pronounced finite signal only in case of the monolayer and bilayer slit pores XS and S, whereas this signal is strongly suppressed for moderate to weak confinement (M, L, and XL) yielding multilayered water lamellae instead. Hence, one can use this ddVSFG signal as a fingerprint not only to distinguish but also to characterize the very specific monolayer and bilayer confinement effects with respect to the multilayer cases which are found to merely be (negative) superpositions of the two bare HBN-water and GRA-water interfaces. Figure S7: Double difference VSFG spectra, see text, for all asymmetric GRA-HBN slit pores. The zero intensity line is shown by a thin solid line. S15

Spectral Decomposition of VSFG Spectra of Confined Water
Based on the understanding from the rigorous theoretical analyses as discussed in the main text, we now fully outline the proposed spectral decomposition technique based on Lorentzian fittings of spectra to understand the VSFG response from confined water.
Lorentzian functions are well known to describe the VSFG spectral lineshapes for bare interfacial water. 9,18 The (complex) Lorentzian function B k /(ω − ω k + iΓ k ) is fully defined by three characteristic parameters, namely the weight B k related to the spectral density, the center frequency ω k and the linewidth Γ k of the k-th oscillator. As shown in Fig. S8 we can fit very well the spectra from both, bare HBN-water and GRA-water interfaces using the following superposition of three Lorentzian functions, The  For the confined water VSFG spectra, we have already shown based on detailed theoretical analyses that the overall spectra are shaped as a result of extensive cancellation Based on that observation, we now introduce a model equation that is the difference between the Lorentzian functions introduced above which characterize the HBN-water (H) and GRA-water (G) interfaces as follows, Thus, both the central frequencies and linewidths are considered to be fixed as determined above for the bare interfaces whereas the spectral weights are adjusted to reproduce best the lineshape function computed for the confined systems. As listed in Table S3, the spectral weights for the moderate to weakly confined multilayer systems (M, L, XL) are found to be very similar to those of the the two bare interfaces. This implies that the corresponding VSFG spectra depicted in Fig. S9(b) are very close to the difference VSFG spectrum of the two bare interfaces as already discussed based on Fig. S6(c) where not much confinement effects are found (see main text). In stark contrast, for the bilayer slit pore S the contribution from the H-bonded region is found to be dramatically reduced.

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Moreover, in case of the monolayer system XS that contribution it even close to fully suppressed such that the contribution from the dangling O-H region is predominant in the VSFG spectrum. The analysis visualized in panel (a) of Fig. S9 supports and quantifies the qualitative discussion of the very pronounced and distinct confinement effects on water within the very narrow slit pores XS and S in the main text. Figure S9: Lorentzian fits of the VSFG spectra of all asymmetric HBN-GRA slit pores. The zero intensity line is shown by a thin solid line. Hence, using the introduced fitting technique, one can easily and quantitatively decompose the VSFG spectral lineshape of confined water in terms of the different mechanistic contributions such as H-bonded versus free O-H water molecules. Importantly, this quantitative analysis can also be carried out using purely experimental means -provided only that the VSFG spectra of the two bare interfaces that are used to confine water within the S18 slit pore setup are known from standard VSFG measurements. The technique ultimately allows one to spectroscopically distinguish the strong confinement effects -as only seen in monolayer and bilayer water lamellae -from multilayer water.